We only need to identify the span of the column space of \({\mathbf {\Gamma }}\)  from minimizing the above objective function. We use the 1D algorithm [1]} to obtain \(\widehat{\mathbf {\Gamma }}\) , where \(\mathrm {span}(\widehat{\mathbf {\Gamma }})\)  is a \(\sqrt{n}\) -consistent estimator of \(\mathrm {span}(\mathbf {\Gamma })\) , rather than MLE (more details on 1D algorithm is given later in the Supplementary Material). In our simulation studies in Section , our 1D algorithm is feasible and fast converging.
